arXiv:2611.09585v1 Announce Type: new Abstract: Space-air-ground integrated networks (SAGINs) integrate heterogeneous communication and computing resources to support ubiquitous services. Service function chains (SFCs) enable complex services to be composed of ordered functions and executed collaboratively across these resources. Mobility continuously reshapes connectivity throughout service execution, yet much of the resulting topology evolution is predictable. Decisions based only on isolated topology snapshots may therefore overlook valuable future connectivity. We formulate an admission-first, cost-aware model on a time-expanded graph for SFC deployment. Our key observation is that temporal feasibility is request-specific, whereas global coupling arises mainly from shared-resource competition. We therefore develop a configurable column-generation framework in which complete request deployments form columns and a restricted master problem coordinates admission and resources. SAGINFE, a fast constructive heuristic built on per-flow embedding (PFE), supplies a standalone feasible solution and initial columns. Configurable pricing schedules combine early-terminated and stricter searches, supplemented by selective PFE candidates. Candidates undergo feasibility and exact reduced-cost checks. Request-wise pricing can run in parallel, followed by finite-pool integer selection. The default configuration improves the admission-first objective over initialization on all 120 main instances. Four pricing workers achieve up to a 2.69-fold median pricing-stage speedup while preserving admitted request counts in the tested cases.